Stability analysis of mathematical model (sirb) in the spread of cholera with vaccination and disinfection

Abstract

Cholera is a disease as a kind of acute diarrhea caused by bacteria V. Cholerae. The spread of cholera can be modeled in the form of nonlinear differential equation systems with 4 variables SIRB. This paper aims to research to analyze the local stability of the equilibrium point of the dynamical population in the spread of cholera by the Routh-Hurwitz stability criterion and bifurcation method. Next Generation Matrix (NGM) method is used to get the basic reproductive numbers ( ℜ0 ) to find the local stability at the equilibrium point of the. The disease-free equilibrium point is locally asymptotically stable if ℜ0 < 1, while the endemic equilibrium point is locally asymptotically stable if ℜ0 > 1 the results of numerical simulations obtained ℜ0 = 0 0.87 indicated that the disease-free equilibrium point is locally asymptotically stable. In endemic condition ( ℜ0 > 1 ) show that increasing the rate of vaccination and disinfection can reduce the population of susceptible, infected and bacteria of V. Cholerae.